(Solved): (NOTE: IN ORDER TO GET FULL MARKS, SHOW ALL CALCULATIONS AND STEPS. FAILURE TO DO SO WILL RESULT I ...

(NOTE: IN ORDER TO GET FULL MARKS, SHOW ALL CALCULATIONS AND STEPS. FAILURE TO DO SO WILL RESULT IN A SCORE OF "O".) The York Plus help line allows students to call and receive assistance in solving their various issues. However, because of the volume of calls, students frequently are put on hold. One of the help line centres claims that 10,000 students call and among them 4,000 callers are put on hold. Suppose that 20 students call. a) What is the proportion that at least two but no more than eight callers are put on hold? b) What is the proportion that less than four and more than six callers are put on hold? c) What is the expected number of callers that are not put on hold? d) Now suppose another help line centre claims that 3500 callers are put on hold instead of 4000 callers. Find the probability that exactly nine callers are put on hold if 20 students called?